1. Field of the Invention
The present invention relates to photonic crystals, and more particularly, to a photonic structure in which a curved optical waveguide, such as a spiral optical waveguide, can be formed.
2. Description of the Related Art
Artificial structural members in which the refractive index is changed periodically are called photonic crystals. Since photonic crystals can highly control light, they are expected to be used for next-generation optical devices. Due to their periodicity, photonic crystals have band structures called photonic bands, as solids have electronic-energy band structures. A gap between photonic bands is called a photonic band gap. Light falling in a wavelength band corresponding to the photonic band gap cannot propagate through the photonic crystal. When a line-shaped defect region is provided in photonic crystal having the photonic band gap, however, the light falling in a wavelength band corresponding to the photonic band gap can be guided along the line-shaped defect region because the light is confined in the defect region by a photonic band gap effect.
Conventionally, photonic crystals having translational symmetry in their refractive-index periodic structures similar to that in solid crystal periodic structures have been extensively researched (for example, see “Photonic Crystals: Molding the Flow of Light” J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Princeton University Press, 1995). As for two-dimensional photonic crystals having translational symmetry, the periodic structures of tetragonal lattices and triangular lattices have been examined. FIG. 20A shows an example two-dimensional photonic crystal having a tetragonal lattice. Rods 11 having a high refractive index are arrayed in air. A photonic band gap appears when the array period, radius, and refractive index of the rods 11 are appropriately selected. FIG. 20B shows an example fundamental structure of an optical waveguide 12 formed in the two-dimensional photonic crystal having the tetragonal lattice. The optical waveguide 12 is formed by removing lines of the rods 11 having a periodic structure. Light propagates through the removed lines of rods 11. The optical waveguide 12 can be a straight line, but even when it has a corner as shown in FIG. 20B, it can guide light with low loss. The bending angle of an optical waveguide is specified by the periodicity of the crystal. It is 90 degrees for tetragonal lattices and 120 degrees for triangular lattices.
Photonic structures having no translational symmetry have also been researched. A photonic structure having rotational symmetry and periodicity defined by a polar coordinate system is disclosed, for example, in Japanese Patent Application Laid Open No. 2003-139978. This photonic structure, called a polar-coordinate-system photonic crystal, has no translational symmetry, but has periodicity in the radial direction and the circumferential direction in the polar coordinate system. A photonic band gap was observed in a polar-coordinate-system photonic crystal having five-fold rotational symmetry. It is shown that it is possible to form not only a straight-line-shaped optical waveguide but an arc-shaped optical waveguide, which is impossible to form in translationally symmetric lattices (such as tetragonal lattices and triangular lattices).
A photonic structure having no periodicity was also reported, for example, by Hiroshi Miyazaki, OYO BUTURI, Volume 74, pp. 202-207 (2005), published by the Japan Society of Applied Physics. This photonic structure is called an amorphous photonic-crystal material. It is shown that a photonic band gap exists even without periodicity. The light-guiding characteristics of a bent optical waveguide having a straight-line defect region was examined.
In an optical circuit in which a light emitting device, a light receiving device, an optical modulation device, and other devices are integrated, optical waveguides are used to exchange light among the devices. When photonic-crystal optical waveguides are used, since the optical waveguides can be bent sharply, the optical circuit can be made compact. In that case, curved optical waveguides are effective because the incident and exit angles of the light and the guide distances can be controlled. In particular, spiral optical waveguides or optical waveguides having curves that are parts of spirals are effective because the radius of curvature can be changed.
When the optical fiber part of a fiber optic gyroscope (hereinafter called an FOG) can be replaced with a photonic-crystal optical waveguide, the FOG is reduced in size. Since the sensitivity of the FOG is proportional to the area enclosed by the optical fiber part, when a photonic-crystal optical waveguide is used instead of the optical fiber part, it is necessary that the optical path length per unit area in the plane be made longer. It is effective to form the photonic-crystal optical waveguide in a spiral shape.
Conventionally, however, when it is attempted to make a spiral optical waveguide in a periodic structure with a two-dimensional tetragonal lattice or triangular lattice, the flexibility of shape design is low and a smooth curve cannot be obtained because optical waveguides can be bent only at specific bending angles such as 90 degrees or 120 degrees.
Conventionally, in polar-coordinate-system photonic crystals, rods constituting a concentric circuit can be removed to form a circular optical waveguide. However, the shape cannot be made spiral.
In amorphous photonic structures, it has been confirmed that a photonic band gap exists even when rods having a high refractive index are arranged at random in a material having a low refractive index. When some of the rods arranged at random are removed to form an optical waveguide, however, it has been shown that good guiding characteristics cannot be obtained. To improve the guiding characteristics, it is known that it is necessary to array rods at both sides of the optical waveguide in a straight line and periodically. If this measure is taken, the rod arrangement becomes the same as that of an optical waveguide formed in a photonic structure having translational symmetry. Little research has been conducted concerning the guidelines for forming an optical waveguide having a desired shape in amorphous photonic structures having no translational symmetry.